Georg Manten

Georg Manten, Cecilia Casolo, Emilio Ferrucci et al.

Inferring the causal structure underlying stochastic dynamical systems from observational data holds great promise in domains ranging from science and health to finance. Such processes can often be accurately modeled via stochastic differential equations (SDEs), which naturally imply causal relationships via "which variables enter the differential of which other variables". In this paper, we develop conditional independence (CI) constraints on coordinate processes over selected intervals that are Markov with respect to the acyclic dependence graph (allowing self-loops) induced by a general SDE model. We then provide a sound and complete causal discovery algorithm, capable of handling both fully and partially observed data, and uniquely recovering the underlying or induced ancestral graph by exploiting time directionality assuming a CI oracle. Finally, to make our algorithm practically usable, we also propose a flexible, consistent signature kernel-based CI test to infer these constraints from data. We extensively benchmark the CI test in isolation and as part of our causal discovery algorithms, outperforming existing approaches in SDE models and beyond.

Georg Manten, Cecilia Casolo, Søren Wengel Mogensen et al.

We develop the theory linking 'E-separation' in directed mixed graphs (DMGs) with conditional independence relations among coordinate processes in stochastic differential equations (SDEs), where causal relationships are determined by "which variables enter the governing equation of which other variables". We prove a global Markov property for cyclic SDEs, which naturally extends to partially observed cyclic SDEs, because our asymmetric independence model is closed under marginalization. We then characterize the class of graphs that encode the same set of independence relations, yielding a result analogous to the seminal 'same skeleton and v-structures' result for directed acyclic graphs (DAGs). In the fully observed case, we show that each such equivalence class of graphs has a greatest element as a parsimonious representation and develop algorithms to identify this greatest element from data. We conjecture that a greatest element also exists under partial observations, which we verify computationally for graphs with up to four nodes.